Fractionation Processes Research Articles

Asian Rainbow Option Pricing Problem Based on Uncertain Fractional Differential Equations

Option pricing is a core issue in option trading, which directly affects investors’ trading decisions and risk management. With the growing maturity of uncertainty theory, the research on option pricing problems based upon uncertainty theory has been gradually deepened. However, the volatility of stock price is not only related to the price at the current moment, but also related to all the previous stock price changes. Uncertain fractional differential equations can well portray the memory and history dependence of financial markets. Its nonlocal nature can more accurately describe the long-term memory effect and the phenomenon of spiky fat tails of stock market fluctuations. Thus, this paper mainly explores the pricing of Asian rainbow option in uncertain financial environments, where the underlying asset price is viewed as uncertain fractional processes. First, two models are presented for discussing the price of Asian rainbow option in two-asset cases, respectively. Then the pricing problems of different types of Asian rainbow options under [Formula: see text]-assets case are further discussed. Finally, empirical analysis is conducted on the proposed models with real stock data to verify the validity of the pricing formulas.

Measuring the 34S and 33S Isotopic Ratios of Volatile Sulfur during Planet Formation

Stable isotopic ratios constitute powerful tools for unraveling the thermal and irradiation history of volatiles. In particular, we can use our knowledge of the isotopic fractionation processes active during the various stages of star, disk, and planet formation to infer the origins of different volatiles with measured isotopic patterns in our own solar system. Observations of planet-forming disks with the Atacama Large Millimeter/submillimeter Array (ALMA) now readily detect the heavier isotopologues of C, O, and N, while the isotopologue abundances and isotopic fractionation mechanisms of sulfur species are less well understood. Using ALMA observations of the SO and SO2 isotopologues in the nearby, molecule-rich disk around the young star Oph-IRS 48 we present the first constraints on the combined 32S/34S and 32S/33S isotope ratios in a planet-forming disk. Given that these isotopologues likely originate in relatively warm gas (>50 K), like most other Oph-IRS 48 volatiles, SO is depleted in heavy sulfur, while SO2 is enriched compared to solar system values. However, we cannot completely rule out a cooler gas reservoir, which would put the SO sulfur ratios more in line with comets and other solar system bodies. We also constrain the S18O/SO ratio and find the limit to be consistent with solar system values given a temperature of 60 K. Together these observations show that we should not assume solar isotopic values for disk sulfur reservoirs, but additional observations are needed to determine the chemical origin of the abundant SO in this disk, inform on what isotopic fractionation mechanism(s) are at play, and aid in unraveling the history of the sulfur budget during the different stages of planet formation.

A frequency domain fractional order tilted integral derivative controller design for fractional order time delay processes

AbstractIn real‐time processes, time delays are inherent due to various factors, such as delays in volume, mass, and information transfer, leading to a deterioration in process performance and stability. Therefore, this paper proposes a fractional‐order tilted integral derivative (TID) controller design for stable and unstable fractional‐order processes with time delay, where the optimal controller parameters are designed using a deterministic approach. An inner loop controller is designed using stability analysis and a graphical approach for unstable fractional‐order time delay processes. The proposed approach offers flexibility and fine‐tuning in designing the controller for a specific application. A systematic reference to the disturbance ratio is carried out to assess the disturbance handling capacity of the proposed controller. It shows the sensitivity of the designed controller against disturbances in the frequency spectrum graphically. Numerous performance indices and time‐domain parameters are computed and compared with state‐of‐the‐art techniques to analyze the efficacy. Furthermore, it is validated on the experimental setup of a four‐tank system. Simulation and experimental results demonstrate that the proposed approach outperforms recent techniques in terms of process control and disturbance rejection.

Density of Uranus moons: Evidence for ice/rock fractionation during planetary accretion

Current models suggest the five regular moons of Uranus formed in a single stage from a primary planetary disk or a secondary impact disk. Using latest estimates of moon masses (Jacobson, 2014), we find a power-law relationship between size and density of the moons due to varying rock/ice ratios caused by fractionation processes. This relationship is better explained by mild enrichment of rock with respect to ice in the solids that aggregate to form the moons following Rayleigh law for distillation (Rayleigh, 1896) than by differential diffusion in the disk, although the two mechanisms are not exclusive. Rayleigh fractionation requires that moon composition and density reflect their order of formation in a closed-system circumplanetary disk. For Uranus, the largest and densest moons Titania and Oberon (R ∼ 788 and 761 km, respectively) first formed, then the mid-sized Umbriel and Ariel (585 and 579 km), satellites in each pair forming simultaneously with similar composition, and finally the small rock-depleted Miranda (236 km). Fractionation likely occurred through impact vaporization during planetesimal accretion. This mechanism would add to those affecting the composition of accreting planets and moons in disks such as temporal/spatial variation of disk composition due to temperature gradients, advection, and large impacts. In the outer solar nebula, Rayleigh fractionation may account for the separation of a rock-dominated reservoir, and an ice-dominated reservoir, currently represented by CI carbonaceous chondrite/type-C asteroids and comets, respectively. Potential consequences for Uranus moons' composition are discussed.

Using Rheology and Image Processing to Study the Effects of Cellulose Nanocrystal Sedimentation.

The effect of sedimentation on lyotropic liquid crystalline dispersions is both an interesting subject in colloidal science and is of practical importance for understanding changes that can occur during dispersion storage. This research explored how the seemingly subtle changes in average length resulting from a single sedimentation step affected the rheological properties and self-assembly of aqueous dispersions of sulfated cellulose nanocrystals. Sedimentation of a primarily isotropic aqueous cellulose nanocrystal dispersion for 1 month at ambient conditions resulted in an isotropic top phase and a biphasic bottom phase, which were separated for further study. Both atomic force microscopy measurements and intrinsic viscosities determined via Fedor's equation showed preferential fractionation of longer cellulose nanocrystals (CNCs) to the bottom phase. The effects of this fractionation on dispersion rheology and phase behavior were studied by preparing a range of concentrations from each phase. As expected, the concentration for the isotropic-biphasic phase transition was significantly lower for the bottom phase than for the top phase or parent dispersion. Rheological changes were generally subtle, but significant differences were seen in the storage modulus at concentrations approaching rheological gelation. Most notably, quantitative image processing showed that even this simple, single-step fractionation process had a significant impact on the relative proportion of tactoids and chiral helices with planar and homeotropic anchoring in self-assembled cellulose nanocrystal films. These results highlight the impact that changes in polydispersity due to sedimentation can have on the self-assembly of nanomaterial mesogens.

Inter- and Intra-Annual Variations in Oak Tree Ring δ13C Values across Different Elevations and Their Climatic Responses in Qinling Mountains

The Qinling Mountains, serving as a natural geographical and climatic boundary in China, require comprehensive climatic records to elucidate the trends in climate changes across the country. While stable isotopes in tree rings are widely employed to indicate historical environmental changes, investigations into tree ring isotopes in the Qinling Mountains, particularly within the widespread broad-leaf oaks, remain limited. In this study, we investigated both intra- and inter-annual variations in the δ13C values of tree rings and their correlations with climatic signals over the past two decades for Quercus aliena var. acuteserrata, a dominant species among oak trees on the main peak of the Qinling Mountains. Our results reveal that responses to climate differ among altitudes and individual trees, with trees at higher altitudes exhibiting higher sensitivity to extreme climate, which is low temperatures and rainfall fluctuations during the growth period in intra-annual δ13C variations. Furthermore, the positive correlations are observed between temperature during growing season and both tree growth and the inter-annual δ13C variations. However, the climate signal appears to be hampered by oak-specific factors, such as intense competition among individuals and the age of trees. Therefore, we suggest a more rigorous selection of sampling and propose further investigations into isotopic fractionation processes in oaks for future studies.

Environmental Benefits of Palm Oil Biodiesel Enhancement: Urea Complexation Optimization via RSM

Indonesian commercial biodiesel products are unstable due to polyunsaturated fatty acids (PUFA). The urea inclusion compound (UIC) method is used during the fractionation process on PUFA to enhance its quality. This study aims to determine the effect of temperature, fatty acid ester metal (FAME)/methanol ratio, and crystallization time on increasing the concentration of PUFA concentrates and to produce high-performance biodiesel products with an iodine indicator <30–40 g I2/100 g. According to the most recent research, the UCF phase product is obtained at a combination of temperature and crystallization time of 20 °C and 4 h, respectively. It has an iodine number of 44.01 and an oxidation stability of 18.61 h, which is close to the criteria for high-performance biodiesel (<30 –40 g I2/100 g). Meanwhile, the results of this study obtained a UCF phase product that has an iodine number of 34.18 and yields 86.57% is obtained at a combination of temperature and crystallization time of 20 °C and 6 hr and FAME-methanol ratio of 6, respectively, which is close to the criteria for high-performance biodiesel (<30 –40 g I2/100 g). The longer complexation time and temperature significantly affected the FAME fractionation of the UCF phase.

Noble Gases, Carbon and Nitrogen Isotopes in Different Lithologies of Pesyanoe: Irradiation History and Impact Processes on the Aubrite Parent Body

Abstract We present the results of stepwise crushing and combustion analyses for noble gases, carbon and nitrogen in Pesyanoe aubrite pyroxene lithologies, composed of grey (Px-G) and light (Px-B) enstatites differing in the degree of impact processing and the number of inclusions. Our study identifies three main noble gas endmembers in Pesyanoe: a cosmogenic component, radiogenic 40Ar, and an endmember representing a mixture of solar wind and Q components in variable proportions. Based on petrographic and noble gas data we argue that these gases accumulated in the material during its regolith history and were later redistributed into gas inclusions/voids as the result of an impact event. During impact metamorphism, Px-G acquired its grey color and multiple gas inclusions were formed within it, more than in case of Px-B. Our study demonstrates for the first time: (1) The host phase of gases trapped during shock metamorphism are grains of rock-forming minerals, in particular Px-G, due to the formation of a large number of cracks in the direction of cleavage during brittle deformation, (2) The gas capture is associated not with the final stage of the formation of consolidated fragmental breccia, at which lithification of the fragments occurred, but with one of the intermediate impact events. High amounts of trapped and cosmogenic noble gases are released during the stepwise crushing—significantly higher than in case of any other studied aubrite. Some unusually high 36Ar/132Xe ratios (up to 54 780 versus 22 705 in the solar wind) were discovered during crushing of Px-G. Our preferable explanation of this phenomenon is a specific superposition of noble gas elemental fractionation processes related to the impact cratering of the Pesyanoe parent body. The carbon isotopic composition (δ13C = –21.2 ± 0.2‰, 1σ) is slightly heavier than that of the Bustee aubrite carbon. The combined use of different extraction methods made it possible to determine that the solar type and indigenous (δ15Nindig = –0.1 ± 3.2‰, 1σ) nitrogen components are located in the gas inclusions, whereas the extraneous nitrogen component (~+45‰) is chemically bound. The large cosmic ray exposure age variations (44 and 55 Ma in case of Px-G and Px-B, respectively) and the heterogeneous distribution of solar-type gases in Pesyanoe aubrite point to a diverse irradiation history of the material before breccia formation. Alternatively/additionally, cosmogenic gases (as well as solar and primordial) in Px-G may have became lost and/or partly redistributed into gas inclusions as a result of the impact event.

Constraints of upper crust magmatic processes on the formation of Saindak porphyry Cu deposit: Insights from mineral geochemistry

Upper crustal magmatic processes play a crucial role in linking the magmatic and hydrothermal systems of porphyry deposits, ultimately controlling the generation of ore-forming fluids. Understanding these processes within a magma chamber is essential for deciphering the formation of porphyry deposits. The Saindak deposit, a large porphyry Cu system in the western Chagai belt, features coeval ore-forming and barren magma pulses, providing key insights into the characterization of porphyry systems. In this study, detailed petrographic observations and geochemical analyses of amphibole, plagioclase, and apatite were conducted to unravel the magmatic evolution at Saindak. Based on textural relationships and crystallization sequences, three distinct populations of amphibole in the ore-forming magma were identified. These amphiboles record the entire fractional crystallization process of magma that initially emplaced at a depth of ∼5 km to the connected magma system at ∼2 km. The study of amphibole and apatite reveals that the fertile magma underwent large-scale fluid exsolution in an open system. The simultaneous and rapid depletion of Cu, Cl, S, and H2O in the magma indicates that Cl and S were highly partitioned into the exsolved fluid phase. These elements formed complexes, which effectively concentrated metals in the fluid. Conversely, the barren magma was characterized by either low metal content or limited fluid exsolution within the magma chamber. Overall, we reconstruct the upper crustal magmatic processes at Saindak and conclude that efficient extraction of Cu through fluid exsolution is the key to porphyry deposit formation.

Fractionation of phenolic aldehydes by liquid–liquid extraction and polymer resin adsorption

ABSTRACT The extraction and adsorption characteristics of three phenolic aldehydes with high physicochemical similarity in lignocellulosic biomass hydrolyzate, which are fermentation inhibitors, were investigated. The extraction process considered both physical extraction with two organic solvents and reactive extraction with five basic extractants. In physical extraction, n-hexane was found to be the most suitable organic solvent for selectively separating 4-hydroxybenzaldehyde from the three phenolic aldehydes, and in reactive extraction, trioctylphosphine oxide was identified as the most suitable basic extractant for the selective separation of syringaldehyde. In the adsorption process, various neutral polymer resins and anion-exchange polymer resins were employed. Among them, the neutral polymer resin XAD16 was found to be the most suitable for selectively separating 4-hydroxybenzaldehyde. To efficiently separate and concentrate the three phenolic aldehydes with equal mass percentages, a proposed five-step fractionation process included the aforementioned extraction and adsorption techniques. By implementing n-hexane-based physical extraction in step 4 and NaOH solution-based back-extraction in step 5 of the fractionation process, the purities of 4-hydroxybenzaldehyde, vanillin, and syringaldehyde in the final solution increased from their initial 33.3% each to 67.6%, 69.8%, and 76.4%, respectively, at a volume ratio of the aqueous phase to the organic phase of 1:15.

Mittag–Leffler Fractional Stochastic Integrals and Processes with Applications

We study Mittag–Leffler (ML) fractional integrals involved in the solution processes of a system of coupled fractional stochastic differential equations. We introduce the ML fractional stochastic process as a ML fractional stochastic integral with respect to a standard Brownian motion. We provide some representation formulas of solution processes in terms of Mittag–Leffler fractional integrals and processes. Computable expressions of the mean functions and of the covariances of such processes are specifically given. The application in neuronal modeling is provided, and all involved functions and processes are specifically determined. Numerical evaluations are carried out and some results are shown and discussed.

Geochemical behavior of riverine magnesium isotopes in the Yarlung Tsangpo River Basin, southern Tibetan Plateau

The riverine magnesium (Mg) isotope composition is generally controlled by sources and fractionation processes. However, it remains unclear in which cases these factors are predominant at the basin scale. In this study, we investigated the major elements, trace elements, and Mg and strontium (Sr) isotope ratios in the Yarlung Tsangpo River (YTR) Basin, southern Tibetan Plateau (TP), to explore the geochemical behavior of Mg isotopes and the dominant controlling factors. Riverine Mg2+ was shown to derive primarily from the weathering of silicates and carbonates. Riverine δ26Mg, which is first influenced by the mixing of different lithological sources, was detected ranging from −1.63 ‰ to −0.52 ‰. According to the saturation indexes of common Mg-bearing secondary minerals, the basin was divided into two zones. Above Shannan City (Zone I), where river waters mostly were oversaturated with minerals, positive correlations were observed between δ26Mg and the Ca/Mg and Sr/Mg ratios. This indicated that, after mixing, secondary minerals (talc and chlorite), which tend to preferentially incorporate 24Mg, may be formed in most of waters, leading to an increase in riverine δ26Mg values. The Rayleigh and batch fractionation models were fitted with factors ranging from 0.9975 to 0.9997. Below Shannan City (Zone II), where river waters mostly were unsaturated with minerals, riverine δ26Mg was positively correlated with 87Sr/86Sr and negatively correlated with the Ca/Mg, Sr/Mg, and HCO3/Na ratios. This suggested that the riverine δ26Mg were influenced by carbonate dissolution with faster kinetic rates. Our analysis of riverine δ26Mg values in the YTR Basin may be a reference for interpreting the relationships between δ26Mg and δ7Li in river systems worldwide. In minerals-oversaturated waters, secondary mineral formation was shown to lead to isotope fractionation, resulting in a positive correlation between the two parameters, whereas in minerals-unsaturated waters, the δ26Mg and δ7Li values were negatively correlated, possibly due to the predominance of mineral dissolution.

Alcohol pretreatment for depolymerization and fractionation of corn stalk

The development of an efficient pretreatment technology to depolymerize and fractionate lignocellulose into glucan, xylan, and lignin is crucial for lignocellulose biorefinery. In this study, alcohol pretreatments using methanol and pentanol were developed and compared. Based on the solubility of the two alcohols, the methanol and pentanol pretreatments are homogeneous and biphasic, respectively. Carbon flow analysis revealed that 1kg of corn stalk (CS) yielded 111.9g of lignin with the homogeneous pretreatment (lignin yield: 60.0 %), while 149.8g of lignin was obtained with the biphasic pretreatment (lignin yield: 80.3 %). Biphasic pretreatment yielded the lignin with higher activity (more β-O-4 bond content). Additionally, 210.4g and 267.0g of glucose were obtained from the enzymatic hydrolysis of homogeneously and biphasically pretreated CS, respectively, where glucose yields were 53.0 % and 67.2 %, respectively. Fourier Transform infrared spectroscopy and X-ray diffraction were employed to verify the component fractionation results. The Hansen solubility parameter and combined severity factor analysis were used to evaluate the effects of various factors on component fractionation. Nuclear magnetic resonance and mechanistic analyses were performed to explore the process of component fractionation. Overall, we discovered that biphasic pretreatment was significantly better than homogeneous pretreatment in component fractionation, including component recovery and lignin activity.

Generalized Fractional Risk Process

Generalized Fractional Risk Process

New bulk rock and age data on the changes in magma evolution during the Miocene, Galatean volcanic area, central Anatolia, Turkey: A review

The Galatean Volcanic Province (GVP) lies within the Sakarya tectonic belt in the northwest of central Anatolia, Turkey, south of the North Anatolian Fault, cropping out over 12,000 km2. It consists of Early Miocene intermediate to acid lavas, pyroclastic rocks, volcaniclastic deposits, and Late Miocene OIB-like basalts. Our study is based on new bulk geochemistry, SrNd isotopes, and 40Ar/39Ar dating of the volcanic rocks from the south-western part of GVP, but integrates all the available previous data to understand how magmas evolved in the post-collisional geodynamic condition in the GVP. The initial eruptions were rhyolitic, as domes or pyroclastic deposits (Group 1) and basaltic lavas (Group 2) during the Early Miocene. Group 2 is also represented by large volumes of basaltic-andesitic, trachyandesite-dacite/trachydacite lava flows, small intrusions, and pyroclastic deposits as generated between 21 and 14 Ma. Relatively low 87Sr/86Sr ratios (0.705–0.706) of the early rhyolites (Group 1), similar to all the rocks from Group (2), suggest the generation of hybrid melts with variable contributions of mantle-derived and crustal material. The volcanic activity ends with OIB-like basalts (11–7 Ma) showing the lowest 87Sr/86Sr (∼0.703) suggesting an asthenospheric origin.The geodynamic model, based on post-Cyprian slab rollback, results in long-term (22–13 Ma) post-collisional delamination/drip processes that support magmatism. This magmatism is generated in the lithospheric mantle, with the formation of basaltic melts and acid hybrid melts showing variable contributions of mantle-derived and crustal materials in a complex trans-crustal magma plumbing system. Complex mixing of various intra-crustal magmas and fractional crystallization processes generated a huge volume of volcanic rocks. The Late Miocene small-volume OIB basalts were asthenospheric melts that during the late stage recorded localized decompression melting processes.

Multivariate Accelerated Degradation Modeling and Reliability Assessment for Ball Screw Grease Based on Fractional Brownian Motion Process Model

Multivariate Accelerated Degradation Modeling and Reliability Assessment for Ball Screw Grease Based on Fractional Brownian Motion Process Model

40 Ar/ 39 Ar chronostratigraphy and geochemistry of Harrats Ishara and Kura in the Hamd–Jizl Basin, Madinah, Saudi Arabia

An extensive system of mafic dykes, volcanic centers, and provincial flood basalts (harrat) have erupted within the Arabian flank of the Red Sea rift since the early Oligocene. The age, spatial distribution, and composition of these features correlates with distinct changes in rift flank structural architecture as the margin progressed through successive deformational phases. A widespread pre-rift dyke swarm in the proto-Red Sea region c. 25 Ma created thermomechanical crustal conditions favourable for diffuse continental rifting and inboard extensional strain markers like the Hamd–Jizl Basin (HJB) originated amagmatically c. 23 Ma. Six million years later, basalt flows from Harrats Ishara and Kura entered the HJB at several points along strike during a 4.5 million year-long eruptive phase. Two distinct volcanic units developed in Harrat Ishara: a predominantly alkali-olivine basalt with an age range of 18.0–14.3 Ma (Ishara A) and a mostly olivine transitional basalt with an age range of 16.6–12.1 Ma (Ishara B). The contemporaneous eruption of these units indicates that multiple magma sources operated simultaneously during the middle Miocene. Both units generally decrease in alkalinity and rare earth element abundances up section, signaling either ongoing melt fractionation processes or output from different magma chambers with time.

Bioassay-Guided Isolation and Identification of Xanthine Oxidase Inhibitory Constituents from the Fruits of Chaenomeles speciosa (Sweet) Nakai.

Chaenomeles speciosa (Sweet) Nakai (C. speciosa) is a traditional Chinese herbal medicine that possesses not only abundant nutritional value but also significant medicinal properties. The extracts of C. speciosa fruits effectively reduce urate levels, but the specific chemical constituents responsible for this effect in C. speciosa fruits are still unknown. Therefore, this study aims to investigate and analyze the structure-activity relationships of these constituents to better understand their ability to lower uric acid. Activity-guided fractionation and purification processes were used to isolate compounds with xanthine oxidase (XO) inhibitory activity from C. speciosa fruits, resulting in three extracts: petroleum ether, ethyl acetate, and n-butanol. The ethyl acetate and n-butanol fractions showed strong activity and underwent further separation and purification using chromatographic techniques. Twenty-four compounds were isolated and identified, with nine showing potent activity, including chlorogenic acid, methyl chlorogenate, butyl chlorogenate, ethyl chlorogenate, cryptochlorogenic acid methyl ester, caffeic acid, p-coumaric acid, benzoic acid and protocatechuic acid. The docking analysis showed that these compounds interacted with amino acid residues in the active site of XO through hydrogen bonding and hydrophobic interactions. These findings suggest that these compounds help reduce uric acid in C. speciosa, supporting further investigation into their mechanism of action.

Pretreatment of Vine Shoot Biomass by Choline Chloride-Based Deep Eutectic Solvents to Promote Biomass Fractionation and Enhance Sugar Production.

Vine shoots hold promise as a biomass source for fermentable sugars with efficient fractionation and conversion processes. The study explores vine shoots as a biomass source for fermentable sugars through pretreatment with two deep eutectic solvents mixtures: choline chloride:lactic acid 1:5 (ChCl:LA) and choline chloride:ethylene glycol 1:2 (ChCl:EG). Pretreatment conditions, such as temperature/time, solid/liquid ratio, and biomass particle size, were studied. Chemical composition, recovery yields, delignification extent, and carbohydrate conversion were evaluated, including the influence of washing solvents. Temperature and particle size notably affected hemicellulose and lignin dissolution, especially with ChCl:LA. Pretreatment yielded enriched cellulose substrates, with high carbohydrate conversion rates up to 75.2% for cellulose and 99.9% for xylan with ChCl:LA, and 54.6% for cellulose and 60.2% for xylan with ChCl:EG. A 50% acetone/water mixture increased the delignification ratios to 31.5%. The results underscore the potential of this pretreatment for vine shoot fractionation, particularly at 30% solid load, while acknowledging the need for further process enhancement.

Stable carbon isotope evolution of formaldehyde on early Mars

Organic matter in the Martian sediments may provide a key to understanding the prebiotic chemistry and habitability of early Mars. The Curiosity rover has measured highly variable and 13C-depleted carbon isotopic values in early Martian organic matter whose origin is uncertain. One hypothesis suggests the deposition of simple organic molecules generated from 13C-depleted CO derived from CO2 photochemical reduction in the atmosphere. Here, we present a coupled photochemistry-climate evolution model incorporating carbon isotope fractionation processes induced by CO2 photolysis, carbon escape, and volcanic outgassing in an early Martian atmosphere of 0.5–2 bar, composed mainly of CO2, CO, and H2 to track the evolution of the carbon isotopic composition of C-bearing species. The calculated carbon isotopic ratio in formaldehyde (H2CO) can be highly depleted in 13C due to CO2-photolysis-induced fractionation and is variable with changes in atmospheric CO/CO2 ratio, surface pressure, albedo, and H2 outgassing rate. Conversely, CO2 becomes enriched in 13C, as estimated from the carbonates preserved in ALH84001 meteorite. Complex organic matter formed by the polymerization of such H2CO could explain the strong depletion in 13C observed in the Martian organic matter. Mixing with other sources of organic matter would account for its unique variable carbon isotopic values.